A multivariate stochastic approach to determine long-term success of SA living annuity portfolios

Abstract

Success rates of living annuities within the South African retirement landscape are examined through portfolio modelling that includes domestic equities, cash, and international exposure, via the S&P 500 index. We define success rates based on Cooley’s framework, emphasising financial sustainability throughout retirement. Our approach incorporates foreign exposure by converting S&P 500 gains to South African Rand, accounting for stochastic foreign exchange rate fluctuations. Additionally, US and South African inflation rates are integrated to assess success rates in real terms, ensuring the impact of inflation on retirees’ income is accurately captured. This study incorporates stochastic correlation and stochastic volatility modelling to capture dynamic asset relationships under varied market conditions. The S&P 500 and JSE Top 40 equities are modelled with stochastic volatility, calibrated through the Efficient Method of Moments (EMM), enhancing volatility estimation for equity assets. These techniques support the analysis of optimal portfolio compositions and withdrawal strategies to maximise annuity success rates, providing evidence-based insights for retirement planning in South Africa.